Is the word deve the same in Brazilian and European Portuguese?

Yes

The word "deve" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It is the third-person singular present indicative of the verb dever, used to express obligation, probability, or debt. The only difference is pronunciation: in Brazilian Portuguese, the final "e" is clearly pronounced as a closed [i] sound, whereas in Continental Portuguese, unstressed final vowels are often reduced or "swallowed," making the "e" sound much more subtle or nearly silent.

Brazilian Portuguese Examples

1. Você deve estudar para a prova. (You must study for the exam.)
2. Ele deve estar dormindo agora. (He must be sleeping now.)
3. A gente deve chegar cedo hoje. (We should arrive early today.)
4. Você me deve dez reais. (You owe me ten reais.)
5. Deve estar muito quente lá fora. (It must be very hot outside.)

Continental Portuguese Examples

1. Tu deves estudar para o exame. (You must study for the exam.)
2. Ele deve estar a dormir agora. (He must be sleeping now.)
3. Nós devemos chegar cedo hoje. (We should arrive early today.)
4. Tu deves-me dez euros. (You owe me ten euros.)
5. Deve estar muito calor lá fora. (It must be very hot outside.)